I use the little terrycloth hairbands to keep my bobbins from unspooling, but then I just toss them into bowls, at least for the ones for my "main" machine. Those are clear plastic so I can see the colors - I have a bowl for fine thread which is all my Aurifil and Presencia thread bobbins, and a separate bowl for thicker thread which is mostly Connecting Threads thread. I also have a really small little dish for polyester - I rarely sew in poly and only keep 3 colors on hand so I don't need much space for those. I never have trouble matching them back up if I want to use matching top & bottom thread, but mostly I match the bobbin thread to the backing fabric so color mismatch doesn't usually matter. I do try to use matching thread weights so I don't have to twiddle around with tension.
For my vintage machines, I usually only have 5-10 bobbins for each machine, so for those I keep the bobbins just loose in the accessory box for the machine they go to, but with those little terrycloth hair bands to keep them from unspooling.